The family at the centre of the sponsorship row surrounding the 19th Sydney Biennale says it has been vilified and is deeply offended by accusations it runs "concentration camps".

Luca Belgiorno-Nettis stepped down from chairing the Biennale last Friday after a group of artists withdrew in protest at his family company, Transfield Holdings, sponsoring what is Australia's largest outdoor art event.

Transfield Holdings is a holding company which has shares in Transfield Services, which won a government contract to supply facilities to the Manus Island detention centre.

"I had no choice [but to resign] in the sense that I'm intimately linked with Transfield," Mr Belgiorno-Nettis told the ABC.

"It's my family company. These activists were calling for a total separation from Transfield. I couldn't see that happening and stay on as chairman."

Nine artists said they would boycott the event unless Biennale severed its relationship with Transfield.

Mr Belgiorno-Nettis says although he and his brother Guido were directors of Transfield Services in the past, they are no longer involved.

"To suggest that we, my family and Transfield are doing something wrong, I don't know," he said.

"That company is doing facilities management. They are basically doing catering, engineering services, plumbing, electrical. Yes, security as well, but basic services. And they're looking to improve those services."

Mr Belgiorno-Nettis said he was worried that if he remained as chairman, the Sydney Biennale would be subject to protests that would ruin the event.

Other major arts organisations face potential protests

A spokesperson for the artists, Gabrielle de Vietri, said artists felt very strongly about what was happening to asylum seekers in Australian detention centres.

"The links between mandatory detention and their involvement through Transfield Holdings was too great to ignore," she said.

"We felt compelled to act and request that that association be cut."

The artists are threatening to target other major arts organisations that receive money from Transfield, including the Art Gallery Of New South Wales, the Museum of Contemporary Art, and the Australian Chamber Orchestra.

Belgiorno-Nettis says he was targeted on social media

As well as the artists' protest, Mr Belgiorno-Nettis was subject to a social media campaign including a wave of tweets accusing him of making money out of "concentration camps" and children in detention.

"It doesn't matter what we say, they are going on, they are still going on, they are calling me intimately linked with human misery, profiting from concentration camps," he said. "What is that?"

The Belgiorno-Nettis family is intimately connected with the Biennale.

Luca's father Franco was founding governor of the Biennale in 1973, and the family has contributed millions, including a $600,000 contribution to this year's $10 million budget.

The event opens next week in many locations in Sydney and will run for three months.